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Simplifying 35 = w2 + 3w Reorder the terms: 35 = 3w + w2 Solving 35 = 3w + w2 Solving for variable 'w'. Reorder the terms: 35 + -3w + -1w2 = 3w + -3w + w2 + -1w2 Combine like terms: 3w + -3w = 0 35 + -3w + -1w2 = 0 + w2 + -1w2 35 + -3w + -1w2 = w2 + -1w2 Combine like terms: w2 + -1w2 = 0 35 + -3w + -1w2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -35 + 3w + w2 = 0 Move the constant term to the right: Add '35' to each side of the equation. -35 + 3w + 35 + w2 = 0 + 35 Reorder the terms: -35 + 35 + 3w + w2 = 0 + 35 Combine like terms: -35 + 35 = 0 0 + 3w + w2 = 0 + 35 3w + w2 = 0 + 35 Combine like terms: 0 + 35 = 35 3w + w2 = 35 The w term is 3w. Take half its coefficient (1.5). Square it (2.25) and add it to both sides. Add '2.25' to each side of the equation. 3w + 2.25 + w2 = 35 + 2.25 Reorder the terms: 2.25 + 3w + w2 = 35 + 2.25 Combine like terms: 35 + 2.25 = 37.25 2.25 + 3w + w2 = 37.25 Factor a perfect square on the left side: (w + 1.5)(w + 1.5) = 37.25 Calculate the square root of the right side: 6.103277808 Break this problem into two subproblems by setting (w + 1.5) equal to 6.103277808 and -6.103277808.Subproblem 1
w + 1.5 = 6.103277808 Simplifying w + 1.5 = 6.103277808 Reorder the terms: 1.5 + w = 6.103277808 Solving 1.5 + w = 6.103277808 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '-1.5' to each side of the equation. 1.5 + -1.5 + w = 6.103277808 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + w = 6.103277808 + -1.5 w = 6.103277808 + -1.5 Combine like terms: 6.103277808 + -1.5 = 4.603277808 w = 4.603277808 Simplifying w = 4.603277808Subproblem 2
w + 1.5 = -6.103277808 Simplifying w + 1.5 = -6.103277808 Reorder the terms: 1.5 + w = -6.103277808 Solving 1.5 + w = -6.103277808 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '-1.5' to each side of the equation. 1.5 + -1.5 + w = -6.103277808 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + w = -6.103277808 + -1.5 w = -6.103277808 + -1.5 Combine like terms: -6.103277808 + -1.5 = -7.603277808 w = -7.603277808 Simplifying w = -7.603277808Solution
The solution to the problem is based on the solutions from the subproblems. w = {4.603277808, -7.603277808}
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